Interpolation Method for Polar Signals in Radio Frequency Transmitters

ABSTRACT

An apparatus for interpolation of polar signals in RF transmitters is disclosed. The apparatus comprises an estimation circuit configured to receive an input in-phase (I) quadrature (Q) signal comprising a plurality of input IQ samples having a first sampling rate associated therewith, and determine a selection metric value indicative of a position of an IQ trajectory associated with one or more input IQ samples of the input IQ signal. The apparatus further comprises a selection circuit configured to receive the input IQ signal and the selection metric value; and adaptively provide the input IQ signal to a first interpolation circuit that implements a first interpolation method or to a second interpolation circuit that implements a second, different interpolation method, for generating interpolated polar samples at a second, different sampling rate, from the input IQ signal, based on the selection metric value.

FIELD

The present disclosure relates to the field of radio frequency (RF)transmitters, and more specifically to an apparatus and a method forinterpolation of polar signals in RF transmitters.

BACKGROUND

RF transmitters utilize RF modulators that modulate an input signal ontoa carrier wave, in order to generate a transmit (Tx) signal at a desiredtransmit frequency. In digital RF transmitters, input sampling rates tothe RF modulator must match an oscillator frequency associated with themodulator. In addition, the spectral replica of a baseband signal mustbe suppressed so that certain spectral requirements are met. Therefore,in RF transmitters, the input signal is upsampled from a baseband rateto an RF rate associated with the oscillator. In particular, in the caseof polar transmitters, the input signal is upsampled and converted topolar domain, thereby generating upsampled polar samples at RF rate,prior to providing the upsampled polar samples to a polar modulator.

BRIEF DESCRIPTION OF THE DRAWINGS

Some examples of circuits, apparatuses and/or methods will be describedin the following by way of example only. In this context, reference willbe made to the accompanying Figures.

FIG. 1 illustrates a simplified block diagram of a polar transmitter,according to one embodiment of the disclosure.

FIG. 2 illustrates an example implementation of a polar transmitter,according to one embodiment of the disclosure.

FIG. 3 illustrates a graphical representation of IQ trajectoriesassociated with an IQ signal in an IQ plane, according to one embodimentof the disclosure.

FIG. 4a and FIG. 4b illustrate the principle of operation thatfacilitates the generation of interpolated polar signals in polartransmitters corresponding to a linear IQ interpolation hereinafterreferred to as a mapped linear interpolation, according to oneembodiment of the disclosure.

FIG. 5 depicts a graph illustrating a correlation between sampling timeoffsets t_(k) of sampling points on a normalized IQ trajectoryassociated with an input IQ signal and the corresponding normalizeddisplacement ξ.

FIG. 6 depicts a simplified block diagram of a mapped linearinterpolation circuit, according to one embodiment of the disclosure.

FIG. 7 depicts a block diagram of a lookup table (LUT) interpolationcircuit, according to one embodiment of the disclosure.

FIG. 8 depicts an example implementation of a lookup table (LUT)interpolation circuit, according to one embodiment of the disclosure.

FIG. 9 illustrates a method of interpolation of polar signals in radiofrequency (RF) transmitters, according to one embodiment of thedisclosure.

FIG. 10 illustrates a method for a linear interpolator circuit,according to one embodiment of the disclosure.

FIG. 11 illustrates a method for a lookup table (LUT) interpolationcircuit, according to one embodiment of the disclosure.

DETAILED DESCRIPTION

In one embodiment of the disclosure, an apparatus for interpolation ofpolar signals in RF transmitters is disclosed. The apparatus comprisesan estimation circuit configured to receive an input in-phase (I)quadrature (Q) signal comprising a plurality of input IQ samples havinga first sampling rate associated therewith; and determine a selectionmetric value associated with a predetermined selection metric, whereinthe selection metric value is indicative of a position of an IQtrajectory associated with one or more input IQ samples of the input IQsignal with respect to the origin of an IQ plane. The apparatus furthercomprises a selection circuit coupled to the estimation circuit, andconfigured to receive the input IQ signal and the selection metricvalue; and adaptively provide the input IQ signal to a firstinterpolation circuit that implements a first interpolation method or toa second interpolation circuit that implements a second, differentinterpolation method for generating interpolated polar samples at asecond, different sampling rate, from the input IQ signal, based on theselection metric value.

In one embodiment of the disclosure, a lookup table (LUT) basedinterpolator circuit is disclosed. The LUT interpolator circuitcomprises a LUT circuit comprising an LUT configured to store aplurality of normalized phase angles or a plurality of normalized radiusvalues or both, wherein each of the normalized phase angle andnormalized radius value has a respective LUT index value associatedtherewith. The LUT interpolator circuit further comprises an addressgenerating circuit configured to receive an input IQ signal comprising aplurality of input IQ samples at a first sampling rate; and generate aset of LUT index values at a second sampling rate, in order to access aset of normalized phase angles or a set of normalized radius values orboth corresponding to the set of LUT index values from the LUT, whereinthe set of LUT index values is generated based on the received input IQsignal and an information of a required interpolation ratio.

In one embodiment of the disclosure, an apparatus for the generation ofinterpolated polar signals in RF transmitters in polar domaincorresponding to a linear interpolation in the IQ domain termed mappedlinear interpolation is disclosed. The apparatus comprises adisplacement calculation circuit configured to receive an input IQsignal comprising a plurality of input IQ samples at a first samplingrate; and determine a set of normalized displacement values associatedwith a normalized displacement, based on the received input IQ signaland an information of a required interpolation ratio. The apparatusfurther comprises an output generation circuit configured to generate aset of interpolated polar samples at a second, different sampling ratebased on a mapping between the set of the normalized displacementvalues, and one or more predefined functions of the normalizeddisplacement indicative of phase angle values or radius values or bothof the interpolated polar samples associated with the input IQ signal.

The present disclosure will now be described with reference to theattached drawing figures, wherein like reference numerals are used torefer to like elements throughout, and wherein the illustratedstructures and devices are not necessarily drawn to scale. As utilizedherein, terms “component,” “system,” “interface,” “circuit” and the likeare intended to refer to a computer-related entity, hardware, software(e.g., in execution), and/or firmware. For example, a component can be aprocessor (e.g., a microprocessor, a controller, or other processingdevice), a process running on a processor, a controller, an object, anexecutable, a program, a storage device, a computer, a tablet PC and/ora user equipment (e.g., mobile phone, etc.) with a processing device. Byway of illustration, an application running on a server and the servercan also be a component. One or more components can reside within aprocess, and a component can be localized on one computer and/ordistributed between two or more computers. A set of elements or a set ofother components can be described herein, in which the term “set” can beinterpreted as “one or more.”

Further, these components can execute from various computer readablestorage media having various data structures stored thereon such as witha module, for example. The components can communicate via local and/orremote processes such as in accordance with a signal having one or moredata packets (e.g., data from one component interacting with anothercomponent in a local system, distributed system, and/or across anetwork, such as, the Internet, a local area network, a wide areanetwork, or similar network with other systems via the signal).

As another example, a component can be an apparatus with specificfunctionality provided by mechanical parts operated by electric orelectronic circuitry, in which the electric or electronic circuitry canbe operated by a software application or a firmware application executedby one or more processors. The one or more processors can be internal orexternal to the apparatus and can execute at least a part of thesoftware or firmware application. As yet another example, a componentcan be an apparatus that provides specific functionality throughelectronic components without mechanical parts; the electroniccomponents can include one or more processors therein to executesoftware and/or firmware that confer(s), at least in part, thefunctionality of the electronic components.

Use of the word exemplary is intended to present concepts in a concretefashion. As used in this application, the term “or” is intended to meanan inclusive “or” rather than an exclusive “or”. That is, unlessspecified otherwise, or clear from context, “X employs A or B” isintended to mean any of the natural inclusive permutations. That is, ifX employs A; X employs B; or X employs both A and B, then “X employs Aor B” is satisfied under any of the foregoing instances. In addition,the articles “a” and “an” as used in this application and the appendedclaims should generally be construed to mean “one or more” unlessspecified otherwise or clear from context to be directed to a singularform. Furthermore, to the extent that the terms “including”, “includes”,“having”, “has”, “with”, or variants thereof are used in either thedetailed description and the claims, such terms are intended to beinclusive in a manner similar to the term “comprising.”

The following detailed description refers to the accompanying drawings.The same reference numbers may be used in different drawings to identifythe same or similar elements. In the following description, for purposesof explanation and not limitation, specific details are set forth suchas particular structures, architectures, interfaces, techniques, etc. inorder to provide a thorough understanding of the various aspects ofvarious embodiments. However, it will be apparent to those skilled inthe art having the benefit of the present disclosure that the variousaspects of the various embodiments may be practiced in other examplesthat depart from these specific details. In certain instances,descriptions of well-known devices, circuits, and methods are omitted soas not to obscure the description of the various embodiments withunnecessary detail.

As indicated above, modulation data or input signal is upsampled fromthe baseband rate to match the RF clock rate associated with an RFoscillator, in digital RF transmitters. In particular, in polartransmitters, the input signal (e.g., an IQ signal) at the basebandsampling rate is upsampled and converted to polar domain, therebygenerating upsampled polar samples at RF sampling rate, prior toproviding the upsampled polar samples to the polar modulator. In thefollowing embodiments, the upsampled polar signals wherever used, aredeemed to have an RF sampling rate. In typical implementation of digitaltransmitters, the baseband clock rate associated with the basebandprocessor is lower than the RF clock rate associated with the polarmodulator and therefore, an arbitrary sampling rate converter (ASRC) isutilized in a transmit chain of the polar transmitters, in order togenerate the upsampled polar samples that match the RF clock rate. Incurrent implementations of the polar transmitters, several interpolationmethods are utilized to generate the upsampled polar samples. Forexample, in a one interpolation method, an input IQ signal is upsampledand interpolated at a lower clock rate (e.g. the baseband clock rate) togenerate upsampled IQ samples at RF sampling rate and the upsampled IQsamples are then converted to polar domain at a higher clock rate (e.g.,the RF rate) to generate the upsampled polar samples. In someembodiments, performing the IQ-to-polar conversion at the higher clockrate is computationally expensive and is therefore not preferred.

Further, in another interpolation method, the IQ-to-polar conversioncomprising converting the IQ signal to polar signal is performed at thelower clock rate, followed by the upsampling of the polar signal togenerate the upsampled polar samples, at the higher clock rate. Eventhough the second interpolation method is not computationally expensive,in some embodiments, high frequency spectral components occur in polarsignals, when an IQ trajectory associated with the IQ signal passesclose to the origin of an IQ plane. Therefore, the second interpolationmethod can only be utilized when the IQ trajectory associated with theIQ signal passes at a particular distance from the origin of the IQplane, as otherwise, undue signal distortion occurs. Furthermore, in ayet another interpolation method, the IQ-to-Polar conversion comprisingconverting the IQ signal to polar signal is performed at the lower clockrate, followed by the upsampling of the polar signal to generate theupsampled polar samples, at the higher clock rate, similar to the secondinterpolation method. Further, a lower radius constraint is utilized inthe third interpolation method, that adds a low pass pulse to the IQtrajectory, in order to divert the IQ trajectory away from the origin,when the IQ trajectory is closer to the origin. However, the lowerradius constraint modifies the actual transmit signal, therebyincreasing error vector magnitude (EVM).

In order to overcome the disadvantages of the above interpolationmethods, an apparatus and a method for interpolating polar signals in RFtransmitters is proposed in this disclosure. In some embodiments, themethod proposed herein adaptively chooses an interpolation method forinterpolating the polar signals, based on an information associated witha position of an IQ trajectory associated with one or more input IQsamples associated with the input IQ signal from the origin of an IQplane. In particular, in one embodiment, the method proposed hereinadaptively chooses an interpolation method for generating interpolated(and/or upsampled) polar samples from the input IQ signal, from a firstinterpolation method comprising a polar interpolation method and asecond, different interpolation method comprising a mapped linearinterpolation method, based on a selection metric value. In someembodiments, the selection metric value is indicative of the position ofthe IQ trajectory associated with one or more input IQ samples of theinput IQ signal with respect to the origin of the IQ plane. In someembodiments, the selection metric value comprises an estimate of adistance of the IQ trajectory associated with the input IQ signal fromthe origin of the IQ plane. Further, in another embodiment, an apparatusand a method for implementing the mapped linear interpolation method isalso proposed.

FIG. 1 illustrates a simplified block diagram of a polar transmitter100, according to one embodiment of the disclosure. The polartransmitter 100 comprises an estimation circuit 102, a selection circuit104, a first interpolation circuit 106 and a second interpolationcircuit 108. In some embodiments, the estimation circuit 102 isconfigured to receive an input IQ signal 110 comprising a plurality ofinput IQ samples at a first sampling rate. In some embodiments, thefirst sampling rate can comprise a baseband rate. Alternately, in otherembodiments, the first sampling rate can comprise a higher sampling ratethan the baseband rate. The input IQ signal 110 comprises an I componentand a Q component associated therewith. However, the I component and theQ component associated with the input IQ signal is not shown here forease of reference. In some embodiments, the estimation circuit 102 isfurther configured to determine a selection metric value associated witha predetermined selection metric, based on the received input IQ signal110. In some embodiments, the selection metric value is indicative of aposition of an IQ trajectory (e.g., the IQ trajectories 310 and 320 inFIG. 3) associated with one or more input IQ samples of the input IQsignal 110 from the origin of an IQ plane. In some embodiments, theestimation circuit 102 is configured to determine the selection metricvalue for each successive IQ trajectory associated with the input IQsignal 110. In some embodiments, the position of an IQ trajectory cancomprise a distance of the IQ trajectory and/or a shape (e.g., acurvature) of the IQ trajectory. In some embodiments, the predeterminedselection metric can comprise an IQ radius comprising a distance (r) ofan IQ trajectory associated with one or more input IQ samples of theinput IQ signal 110 from the origin of an IQ plane. And, in suchembodiments, the selection metric value can comprise an IQ radiusestimate (i.e., an IQ radius value). However, in other embodiments, thepredetermined selection metric can comprise more advanced criteria liker/r″, taking into account a curvature of the IQ trajectory (r″).Further, other predetermined selection metrics are also contemplated tobe within the scope of this disclosure.

The selection circuit 104 is coupled to the estimation circuit 102 andis configured to receive the selection metric value and the input IQsignal 110 from the estimation circuit 102. Therefore, in suchembodiments, an output signal 112 of the estimation circuit comprisesthe input IQ signal 110 and the selection metric value. Upon receivingthe selection metric value, in some embodiments, the selection circuit104 is configured to process the selection metric value and estimate aposition of the IQ trajectory associated with one or more input IQsamples, based on the selection metric value. In some embodiments, theposition of the IQ trajectory is estimated based on a first criteriacomprising, determining if the selection metric value is within a firstpredetermined metric range or a second, different predetermined metricrange. In some embodiments, the first predetermined metric range caninclude a range of values between a predetermined metric threshold and apredetermined value (e.g., zero or any other value) lower than thepredetermined metric threshold. Similarly, the second predeterminedmetric range can include a range of values between the predeterminedmetric threshold and a predetermined value (e.g., any value) higher thanthe predetermined metric threshold. However, in other embodiments, thefirst predetermined metric range can include a range of values betweenthe predetermined metric threshold and a predetermined value (e.g., anyvalue) higher than the predetermined metric threshold. And, the secondpredetermined metric range can include a range of values between thepredetermined metric threshold and a predetermined value (e.g., zero orany other value) lower than the predetermined metric threshold. Forexample, in some embodiments, when the selection metric value comprisesan IQ radius estimate, a selection metric value within the firstpredetermined metric range can indicate that the IQ trajectory is closerto the origin, and a selection metric value within the secondpredetermined metric range can indicate that the IQ trajectory isfarther away from the origin. Further in some embodiments, the positionof the IQ trajectory is estimated based on a second criteria comprising,comparing the selection metric value to a predetermined metric threshold(e.g., the radius threshold 330 in FIG. 3). In some embodiments, whenthe selection metric value comprises an IQ radius estimate, thepredetermined metric threshold provides an indication if an IQtrajectory is close to the origin or farther away from the origin.

For example, a selection metric value less than the predetermined metricthreshold indicates that the IQ trajectory is closer to the origin, anda selection metric value greater than the predetermined metric thresholdindicates that the IQ trajectory is farther away from the origin.Furthermore, in other embodiments, other different criteria forestimating the position of the IQ trajectory associated with one or moreinput IQ samples based on the selection metric value is alsocontemplated to be within the scope of this disclosure. In someembodiments, the selection circuit 104 is further configured toadaptively convey the input IQ signal 110 to the first interpolationcircuit 106 or to the second interpolation circuit 108, based on theselection metric value. For example, in some embodiments, the selectioncircuit 104 can be configured to convey the input IQ signal 110 to thefirst interpolation circuit 106, when the selection metric valueindicates that the IQ trajectory is closer to the origin and convey theinput IQ signal 110 to the second interpolation circuit 108, when theselection metric value indicates that the IQ trajectory is farther awayfrom the origin. However, in other embodiments, the selection circuit104 can be configured to convey the input IQ signal 110 to the firstinterpolation circuit 106 or to the second interpolation circuit 108,based on a different criterion associated with the selection metricvalue.

In some embodiments, the first interpolator circuit 106 is coupled tothe selection circuit 104 and is configured to receive the input IQsignal 110 and implement a first interpolation method for generatinginterpolated polar samples 118 a from the input IQ signal 110. In someembodiments, the second interpolator circuit 108 is coupled to theselection circuit 104 and is configured to receive the input IQ signal110 and implement a second, different interpolation method forgenerating interpolated polar samples 118 b from the input IQ signal110. In some embodiments, the interpolated polar samples 118 a and 118 bare at a second, different sampling rate (e.g., a RF rate) higher thanthe first sampling rate. In some embodiments, the interpolated polarsamples 118 a and 118 b are provided to a polar modulator. At oneinstance, either the interpolated polar samples 118 a or theinterpolated polar samples 118 b are generated, based on theinterpolation circuit chosen, in accordance with the selection metricvalue. In some embodiments, the selection circuit 104 enables toadaptively choose between the first interpolation method and the second,different interpolation method for generating the interpolated polarsamples (e.g., 118 a or 118 b) from the input IQ signal 110, based onthe selection metric value.

FIG. 2 illustrates an example implementation of a polar transmitter 200,according to one embodiment of the disclosure. In some embodiments, thepolar transmitter 200 depicts one possible way of implementation of thepolar transmitter 100 in FIG. 1. In this embodiment, the polartransmitter 200 is similar to the polar transmitter 100 in FIG. 1, withthe first interpolation circuit 106 implemented as a polar interpolationcircuit and the second interpolation circuit 108 implemented as a mappedlinear interpolation circuit. Alternately in other embodiments, thefirst interpolation circuit 106 of the polar transmitter 100 can beimplemented as a mapped linear interpolation circuit and the secondinterpolation circuit 108 of the polar transmitter 100 can beimplemented as a polar interpolation circuit. The polar transmitter 200comprises an estimation circuit 202, a selection circuit 204, a polarinterpolation circuit 206 and a mapped linear interpolation circuit 208.

In some embodiments, the estimation circuit 202 is configured to receivean input IQ signal 210 comprising a plurality of input IQ samples at afirst sampling rate. In some embodiments, the first sampling rate cancomprise a baseband rate. Alternately, in other embodiments, the inputIQ signal 210 is an already upsampled signal and therefore, in suchembodiments, the first sampling rate can comprise a higher sampling ratethan the baseband rate. In some embodiments, the estimation circuit 202is further configured to determine a selection metric value associatedwith a predetermined selection metric, based on the received input IQsignal 210, as explained above with respect to FIG. 1. In someembodiments, the selection metric value is indicative of a position ofan IQ trajectory (e.g. the IQ trajectories 310 and 320 in FIG. 3)associated with one or more input IQ samples of the input IQ signal 210from the origin of an IQ plane. In some embodiments, the position of anIQ trajectory can comprise a distance of the IQ trajectory and/or ashape (e.g., a curvature) of the IQ trajectory. In other embodiments,the position of an IQ trajectory can further comprise other locationspecific characteristics associated with the IQ trajectory.

The selection circuit 204 is coupled to the estimation circuit 202 andis configured to receive the selection metric value and the input IQsignal 210 from the estimation circuit 202. Therefore, in suchembodiments, an output signal 212 of the estimation circuit 202comprises the input IQ signal 210 and the selection metric value. Uponreceiving the selection metric value, in some embodiments, the selectioncircuit 204 is configured to process the selection metric value andestimate a position of the IQ trajectory associated with one or moreinput IQ samples (e.g., determine if the IQ trajectory is closer to theorigin or farther away from the origin, in some embodiments), based onthe selection metric value, as explained above with respect to FIG. 1.The selection circuit 204 is further configured to adaptively providethe input IQ signal 210 to the polar interpolator circuit 206 or to thelinear interpolator circuit 208, based on the selection metric value.For example, in some embodiments, when the selection metric valuecomprises an IQ radius estimate, and when the IQ radius estimateindicates that the IQ trajectory associated with the input IQ signal 210is farther away from the origin (e.g., IQ trajectory 310 in FIG. 3), theselection circuit 204 is configured to provide the input IQ signal 210to the polar interpolation circuit 206 over the selection output path214. Similarly, when the selection metric value comprises an IQ radiusestimate, and when the IQ radius estimate indicates that the IQtrajectory associated with the input IQ signal 210 is closer to theorigin (e.g., the IQ trajectory 320 in FIG. 3), the selection circuit204 is configured to provide the input IQ signal 210 to the mappedlinear interpolation circuit 208 over the selection output path 216.

However, in other embodiments, the selection metric can comprise moreadvanced selection criteria that takes into account othercharacteristics associated with the IQ trajectory, for example, amagnitude of r/r″, taking into account a curvature of the IQ trajectory(r″) apart from the IQ radius r. In such embodiments, both the IQ radiusestimate and the curvature of the IQ trajectory have to be taken intoaccount, before adaptively providing the input IQ signal 210 to thepolar interpolator circuit 206 or to the mapped linear interpolatorcircuit 208. In some embodiments, the position of the IQ trajectory isestimated based on a first criteria comprising, determining if theselection metric value is within a first predetermined metric range or asecond, different predetermined metric range. In some embodiments, thefirst metric range and the second, different metric range arepredetermined, based on the selection metric chosen. Further in someembodiments, the position of the IQ trajectory is estimated based on asecond criteria comprising, comparing the selection metric value to apredetermined metric threshold. In some embodiments, the metricthreshold is predetermined, based on the selection metric chosen.

The polar interpolation circuit 206 is coupled to the selection circuit204 and is configured to upsample and interpolate the input IQ signal210, based on a polar interpolation method. In such embodiments, thepolar interpolation circuit 206 is configured to receive the input IQsignal 210 and generate interpolated and upsampled polar samples 218 aat a second, different sampling rate (e.g., a radio frequency (RF) rate)from the input IQ signal 210. In some embodiments, the sampling rate ofthe interpolated polar samples 218 a is higher than the sampling rate ofthe input IQ signal 210. In some embodiments, the interpolated polarsamples 218 a are further provided to a polar modulator (not shown) forfurther processing. In some embodiments, the polar interpolation circuit206 comprises an IQ-to-polar conversion circuit 206 a (e.g., CORDIC)that operates at a low clock rate (e.g., the baseband rate) and convertthe IQ samples at a low sampling rate associated with the input IQsignal 210 into corresponding polar samples at the low sampling rate(e.g., the baseband rate), thereby forming low rate polar samples 206 c.In some embodiments, the polar interpolation circuit 206 furthercomprises an arbitrary sampling rate converter (ASRC) 206 b configuredto convert the low rate polar samples 206 c to interpolated polarsamples 218 a at the RF rate. In some embodiments, the ASRC 206 boperated at a high clock rate (e.g., the RF rate). In some embodiments,the ASRC 206 b uses a conventional low pass interpolation algorithm togenerate the interpolated polar samples 218 a. However, otherconventional polar interpolation algorithms are also contemplated to bewithin the scope of this disclosure. In some embodiments, the ASRC 206 bperforms the upsampling of the polar signals 206 c at the low rate byvariable fractional factors, in order to generate the interpolated polarsamples 218 a. In some embodiments, the RF rate corresponds to anoscillator frequency associated with the polar modulator and istypically higher than the baseband rate. In some embodiments, the inputIQ signal 210 is upsampled in order to match the RF rate of the polarmodulator.

The mapped linear interpolation circuit 208 is coupled to the selectioncircuit 204 and is configured to upsample and interpolate the input IQsignal 210, based on mapped linear interpolation. In such embodiments,the mapped linear interpolation circuit 208 is configured to receive theinput IQ signal 210 at the lower sampling rate and generate interpolatedand upsampled polar samples 218 b at the higher sampling rate (e.g., theradio frequency (RF) rate) directly from the input IQ signal 210, basedon the mapped linear interpolation. In some embodiments, theinterpolated polar samples 218 b are further provided to a polarmodulator (not shown) for further processing. In some embodiments, themapped linear interpolation circuit 208 is configured to generate theinterpolated polar samples 218 b at the higher sampling rate from theinput IQ signal 210, based on mapped linear interpolation of the inputIQ signal 210 based on one or more predefined functions indicative ofpolar representation of IQ samples. In some embodiments, the mappedlinear interpolation of the input IQ signal 210 is realized based on anormalization of IQ trajectories associated with the input IQ signal210, further details of which are provided in an embodiment below.

In some embodiments, the mapped linear interpolation circuit 208 enablesto generate the interpolated polar samples 218 b from the input IQsignal 210 in an efficient way when the IQ trajectory associated withthe input IQ signal 210 is closer to the origin. When the IQ trajectoryassociated with the input IQ signal 210 is closer to the origin, highfrequency spectral components occur in polar signals which leads toundue signal distortion while utilizing the polar interpolation methodfor interpolating the input IQ signal 210. However, as indicated above,other criteria associated with the IQ trajectory, for example, acurvature associated with the IQ trajectory is also taken intoconsideration, in some embodiments, before choosing an interpolationmethod for generating the interpolated polar samples. That is, even ifthe IQ trajectory is close to the origin, other factors like thecurvature of the IQ trajectory is also considered before choosing theinterpolation method, in some embodiments.

FIG. 4a and FIG. 4b illustrate the principle of operation thatfacilitates to utilize mapped linear interpolation for generatinginterpolated and upsampled polar signals in polar transmitters,according to one embodiment of the disclosure. In some embodiments, theprinciple of operation explained herein is utilized within the mappedlinear interpolation circuit 208 in FIG. 2. However, in otherembodiments, the principle of operation explained herein can be appliedto any interpolation circuit that utilizes mapped linear interpolation.In this embodiment, the principle of operation is explained withreference to the mapped linear interpolation circuit 208 in FIG. 2. FIG.4a illustrates an IQ plane 400 comprising an I axis 401 a and a Q-axis401 b. Let P_(m) 402 and P_(m+1) 404 represent two IQ data pointsassociated with an input IQ signal (e.g., the input IQ signal 210 inFIG. 2), that needs to be converted to interpolated polar samples (e.g.,the interpolated polar samples 218 b in FIG. 2), where m corresponds toa current time index at low sampling rate. Further, vector w 406represents a vector connecting the IQ data points P_(m) 402 and P_(m+1)404, that forms the IQ trajectory 406, and vector v 408 represents anormal vector to the IQ trajectory 406 having an angle ϕ₀ 410 associatedtherewith.

The goal of the mapped linear interpolation circuit (e.g., the mappedlinear interpolation circuit 208 in FIG. 2) is to generate upsampledpolar samples at higher rate (corresponding to the sampling points 403a, 403 n etc. on the vector w 406) in polar domain, from the input IQsignal (e.g., the input IQ signal 210 in FIG. 2) based on mapped linearinterpolation. In order to achieve this, the IQ trajectory 406 needs tobe normalized. FIG. 4b illustrates an IQ plane 450 comprising an I axis451 a and a Q-axis 451 b. In some embodiments, the IQ plane 450 is thesame as the IQ plane 400 in FIG. 4a and is utilized herein to illustratethe effect of normalization of the IQ trajectory 406 in FIG. 4a . FIG.4b illustrates a normalized IQ trajectory w* 452, formed based onnormalizing the IQ trajectory 406 in FIG. 4a . In some embodiments, thenormalized IQ trajectory w* 452 is obtained based on rotating the normalvector v 408 by an angle ϕ₀, onto the l-axis, thereby forming the vectorv* 454 in FIG. 4b . Therefore, in such embodiments, the IQ data pointsP_(m) 402 and P_(m+1) 404 in FIG. 4a are also rotated by the same angleto form the IQ data points P_(m)* 456 and P_(m+1)* 458. In thisembodiment, the IQ trajectory 406 is normalized based on rotating thenormal vector v 408 by an angle ϕ₀, onto the l-axis. However, in otherembodiments, the IQ trajectory 406 can be normalized based on rotatingthe normal vector v 408 by an angle ϕ₀, onto the Q-axis. From thenormalized IQ trajectory w* 452, one can obtain the following IQtrajectory parameters of the IQ trajectory w 406, that is, an IQdistance d comprising a distance of w 406 from the origin, IQ trajectorylength l comprising a length of w 406, an IQ offset a comprising anoffset of w 406 and a rotation angle ϕ₀ comprising an angle of vector v408. In some embodiments, the IQ trajectory parameters are generated byutilizing a coordinate rotation digital computer (CORDIC).

The key idea utilized herein that enables to utilize mapped linearinterpolation to generate the interpolated polar samples (e.g., theinterpolated polar samples 218 b in FIG. 2), is that, when a linearconnection of two IQ samples (e.g., the IQ trajectory 406 in FIG. 4a )associated with an input IQ signal is normalized to form an angle anddistance normalized IQ trajectory (e.g., the angle normalized IQtrajectory w* 452 can be seen in FIG. 4b ), a normalized polarrepresentation of the high rate sampling points can be drawn frompredefined constant functions. Therefore, the phase angles and radiusvalues (i.e., the polar representation) for the sampling points (e.g.,the sampling points 403 a, 403 n etc. on the vector w 406) for an IQtrajectory (e.g., the IQ trajectory 406 in FIG. 4a ) can be obtainedbased on the normalized polar representation of the sampling points ofthe normalized IQ trajectory, in accordance with the predefined constantfunctions.

For example, from the normalized IQ trajectory w* 452 in FIG. 4b , forany sampling point (e.g., the sampling point 453 a) at a displacement ofx from the l-axis 451 a, the phase values V along the normalized IQtrajectory w* 452 based on linear IQ interpolation, can be defined asgiven below:

$\begin{matrix}{\Phi^{*} = {- {\arctan ( \frac{x}{d} )}}} & (1)\end{matrix}$

Where ϕ* is defined herein as a normalized phase angle, x is thedisplacement of the sampling points on the vector w* 452 from the l-axis451 a and d is the distance of w* 452 from the origin.Therefore, a phase ϕ along the original vector, that is the IQtrajectory w 406 is given by:

ϕ=ϕ₀+ϕ*  (2)

Substituting x/d=ξ, a normalized displacement  (3)

The phase ϕ can be written as,

ϕ=f(ξ)=ϕ₀−arctan(ξ)  (4)

thus, from equation (4), it can be seen that the phase angle ϕ for anyIQ sampling point along an IQ trajectory (e.g., the IQ trajectory 406 inFIG. 4a ) can be derived from a rotation angle ϕ₀ obtained from therotation of a normal vector (e.g., the normal vector v 408 in FIG. 4a )and a function of ξ, for example, arctan(ξ).

Similarly, from FIG. 4b , radius values r for any sampling point (e.g.,the sampling point 453 a) at a displacement of x from the l-axis 451 aalong the normalized IQ trajectory 452 based on liner IQ interpolation,can be defined as given below:

$\begin{matrix}{r = {\sqrt{d^{2} + x^{2}} = {d\sqrt{1 + \frac{x^{2}}{d^{2}}}}}} & (5)\end{matrix}$

Where x is the displacement of the sampling points on the vector w* 452from the l-axis 451 a and d is the distance of w* 452 from the origin.In some embodiments, the radius values r for the sampling points alongthe normalized IQ trajectory w* 452 in FIG. 4b is same as the radiusvalues for the sampling points along the IQ trajectory w 406 in FIG. 4a. Further, in some embodiments, the radius values r can also be definedin terms of the normalized displacement as given below:

r=f(ξ)=d√{square root over (1+ξ²)}=d·r*  (6)

where r* is defined herein as a normalized radius value. Thus, fromequation (6), it can be seen that the radius value r for any IQ samplingpoint along an IQ trajectory (e.g., the IQ trajectory 406 in FIG. 4a )can be derived based on the distance d of w* 452 from the origin and afunction of ξ, for example, r*=√{square root over (1+ξ²)}.

Therefore, from above, it can be seen that the phase angles ϕ of thesampling points of the IQ trajectory (e.g., the IQ trajectory 406 inFIG. 4a ) for any IQ signal can be derived from an information of therotation angle ϕ₀ and the normalized displacement ξ, based on equation(4). Similarly, it can be seen that the radius value r of the samplingpoints of the IQ trajectory (e.g., the IQ trajectory 406 in FIG. 4a )for any IQ signal can be derived from an information of the distance dand the normalized displacement ξ, based on equation (6). In someembodiments, the rotation angle ϕ₀ and the distance d for an input IQsignal (e.g., the input IQ signal 210) can be derived based on anormalization of the IQ trajectory (e.g., the IQ trajectory 406 in FIG.4b ) associated with the input IQ signal. Further, the normalizeddisplacement corresponding to each sampling point (e.g., the samplingpoints 403 a, 403 n etc. on the IQ trajectory 406 in FIG. 4a ) on the IQtrajectory (e.g., the IQ trajectory 406 in FIG. 4b ) is to bedetermined, the details of which are given in FIG. 5 below. In someembodiments, the normalized displacement ξ can be determined based on aninformation of a location of the sampling points (x value) along theangle normalized IQ trajectory (e.g., the angle normalized IQ trajectoryw* 452 in FIG. 4b ). Therefore, in order to generate upsampled polarsamples (e.g., the interpolated polar samples 218 b in FIG. 2) from aninput IQ signal (e.g., the input IQ signal 210 in FIG. 2), a mappedlinear interpolator circuit (e.g., the mapped linear interpolatorcircuit 208 in FIG. 2) can be configured to normalize an IQ trajectoryassociated with the input IQ signal, determine a normalized displacementξ corresponding to each sampling point on the IQ trajectory, anddetermine the corresponding phase angle and radius values (i.e., theinterpolated polar samples) based on equations (4) and (6) above,respectively. In some embodiments, the mapped linear interpolatorcircuit is configured to normalize a plurality of IQ trajectoriesassociated with the input IQ signal, in order to generate interpolatedpolar samples corresponding to a respective IQ trajectory of theplurality of IQ trajectories.

FIG. 5 depicts a graph 500 illustrating a correlation between samplingtime offsets t_(k) of sampling points (corresponding to RF outputsamples 502, 504, 506 etc.) on an angle normalized IQ trajectoryassociated with an input IQ signal and the corresponding normalizeddisplacement ξ. A time offset t=0 (axis 510 in FIG. 5) corresponds tothe time of the first IQ sample P_(m) of the IQ trajectory section P_(m)to P_(m+1) and a time offset t=1 corresponds to the time of the secondIQ sample P_(m+1). The correlation in the graph 500 is derived based onthe angle normalized IQ trajectory w* 452 in FIG. 4b . In otherembodiments, the same correlation can be derived based on anglenormalized IQ trajectories of any input IQ signal. In some embodiments,information of a location of the sampling points on the angle normalizedIQ trajectory is required in order to determine the normalizeddisplacement corresponding to each sampling point on the anglenormalized IQ trajectory. The graph 500 comprises a time offset axis t510 that depicts the point in time (to) where the first output sample atthe RF rate for the angle normalized IQ trajectory w* 452 has to begenerated, and the time difference tΔ between the successive RF outputsamples i.e. the interpolated polar samples. In some embodiments, thetime difference t_(Δ) between the successive RF output samples may notbe constant and depends on an interpolation ratio associated therewith.In order to derive the normalized displacement ξ, the sampling timeoffsets t_(k) of the RF output samples have to be mapped to a locationof the corresponding RF output samples along the angle normalized IQtrajectory w* 452. A location axis x 520 is therefore depicted herein toillustrate a mapping of the sampling time offsets of the RF outputsamples to their corresponding location on the angle normalized IQtrajectory w* 452. In some embodiments, the location axis x 520 isfurther scaled by an inverse of d, as depicted by the correlation axis530, in order to derive the correlation between the sampling timeoffsets t_(k) on the time offset axis t 510 and the correspondingnormalized displacement value ξ_(k).

In some embodiments, normalized displacement corresponding to eachsampling points 502, 504, 506 etc. can be derived based on aninformation of the time offset t0 of a first RF output sample, the timedifference tΔ between the successive RF samples and mapping the samplingtime offsets to the correlation axis 530 depicted in the graph 500. Inorder to map the sampling time offsets (i.e., the time offset axis (t))to the correlation axis ξ 530, in some embodiments, information on theIQ trajectory parameters d, l, a (as explained above with respect toFIG. 4b ) is also required. In some embodiments, a time offset for thefirst RF sample to is given by,

t _(0,m)=₀=0  (7)

where m is the time index of the low rate input IQ signal, for example,corresponding to the IQ data point P_(m)* in FIG. 5.Further, the time difference to between the successive RF samples isgiven by,

t _(Δ,m) =n ⁻¹  (8)

Where n is the current interpolation ratio. In some embodiments, theinterpolation ratio corresponds to a ratio of the sampling rate of theRF output samples (i.e., high clock rate) to the sampling rate of theinput IQ samples (i.e., the low clock rate). Here, the interpolationratio n is considered constant within a low rate period. However, inother embodiments, the interpolation ration n can change from RF sampleto RF sample.From equations (7) and (8), a number of RF output samples Km on thecurrent IQ trajectory w* 452 can be derived as given below:

$\begin{matrix}{K_{m} = \lceil \frac{1 - t_{0,m}}{t_{\Delta,m}} \rceil} & (9)\end{matrix}$

Similarly, the time offset for the first RF sample corresponding to thesubsequent IQ trajectory section between IQ sample points P_(m+1)* andP_(m+2)* can be derived as given below:

t _(0,m+1) =t _(0,m) +K _(m) t _(Δ,m)−1  (10)

The above equation shows the relation between the first RF time offsetsof each section t_(0,m) of subsequent IQ trajectory sections.

From the above parameters and from the correlation axis ξ 530,normalized displacement ξ corresponding to the first RF output sample ofthe IQ trajectory section P_(m) to P_(m+1) where subsequently the indexm is omitted for clarity is derived as:

$\begin{matrix}{\xi_{0} = {\frac{1}{d}( {{t_{0}l} - a} )}} & (11)\end{matrix}$

anda difference in normalized displacement ξ_(Δ) between successive RFsamples is derived as:

$\begin{matrix}{\xi_{\Delta} = {\frac{1}{d}( {t_{\Delta}l} )}} & (12)\end{matrix}$

From ξ₀ and ξ_(Δ), the normalized displacement value ξ_(k) correspondingto each RF output sample 502, 504, 506 etc. can be derived as givenbelow:

ξ_(k)=ξ₀ +kξ _(Δ); 0≤k<K  (13)

Where K (i.e. K_(m) in equation (9)) is the number of RF output sampleson the current IQ trajectory.Once the normalized displacement value ξ_(k) corresponding to each RFoutput sample 502, 504, 506 etc. is determined, the corresponding phaseangles and radius values for the RF output samples on the originalvector w 406 in FIG. 4a can be determined based on equations (4) and (6)above.

In one embodiment, the arctan(ξ) function in equation (4) and the√{square root over (1+ξ²)} function in equation (6) are realized using alookup table (LUT). In such embodiments, the mapped linear interpolationcircuit comprises a LUT comprising a plurality of normalized phaseangles arctan(ξ) and a plurality of normalized radius values √{squareroot over (1+ξ²)}, for a plurality of predetermined values of ξ, thedetails of which are given in an embodiment below. However, in otherembodiments, the arctan(ξ) function in equation (4) and the √{squareroot over (1+ξ²)} function in equation (6) can be realized differently.For example, upon determining the normalized displacement values ξ_(k)according to equation (13), the arctan(ξ) function and the √{square rootover (1+ξ²)} function can be approximated using suitable approximationalgorithms. In some embodiments, the equations (7)-(13) for determiningthe normalized displacement values ξ_(k) are implemented within a mappedlinear interpolation circuit (e.g., the mapped linear interpolationcircuit 208 in FIG. 2).

FIG. 6 depicts a simplified block diagram of a mapped linearinterpolation circuit 600, according to one embodiment of thedisclosure. In some embodiments, the mapped linear interpolation circuit600 can be included within the mapped linear interpolation circuit 208in FIG. 2. However, in other embodiments, the mapped linearinterpolation circuit 600 can be part of any other polar transmitter,and can be utilized for generating interpolated polar samples at RF ratefrom an input IQ signal at a lower sampling rate (e.g., baseband rate).In this embodiment, the mapped linear interpolation circuit is explainedwith respect to the mapped linear interpolation circuit 208 in FIG. 2and the principle of operation explained in FIG. 4a , FIG. 4b and FIG.5. The mapped linear interpolation circuit 600 comprises a displacementcalculation circuit 602 and an output generation circuit 604. In someembodiments, the displacement calculation circuit 602 is configured toreceive an input IQ signal 606 (e.g., the input IQ signal 216 in FIG.2). In some embodiments, the input IQ signal 606 comprises a pluralityof input IQ samples having a first sampling rate (e.g., a baseband rateor a lower sampling rate) associated therewith. In some embodiments, thedisplacement calculation circuit 602 is further configured to receive acurrent interpolation ratio 608.

Upon receiving the input IQ signal 606 and the current interpolationratio 608, in some embodiments, the displacement calculation circuit 602is configured to normalize the input IQ signal based on rotating thenormal vectors of IQ trajectories associated with the input IQ signal606 on to an l-axis of a respective IQ plane, as shown in FIG. 4b aboveor to a Q-axis of the respective IQ plane. For each IQ trajectoryassociated with the input IQ signal 606, the displacement calculationcircuit 602 is further configured to determine IQ trajectory parameterscomprising an IQ distance d, IQ trajectory length l, an IQ offset a anda rotation angle ϕ₀, as explained above with respect to FIG. 4a above.In some embodiments, the IQ trajectory parameters can be determined atthe displacement calculation circuit 602 by using a coordinate rotationdigital computer (CORDIC). Upon determining the IQ trajectoryparameters, the displacement calculation circuit 602 is configured todetermine a plurality of normalized displacement values ξ_(k) based onimplementing the equations (7)-(13) above. In some embodiments, thedisplacement calculation circuit 602 can comprise an arithmetic circuit602 a configured to determine the IQ distance d, the IQ trajectorylength l, the IQ offset a and the rotation angle ϕ₀. In someembodiments, the arithmetic circuit 602 a can be further configured toimplement the equations (7)-(12) above. In some embodiments, thedisplacement calculation circuit 602 can further comprise an integratorcircuit 602 b to implement equation (13). In some embodiments, theintegrator circuit 602 b is configured to generate the plurality ofnormalized displacement values ξ_(k) at a second, different samplingrate (e.g., the RF rate or a higher sampling rate).

The output generation circuit 604 is coupled to an output of thedisplacement calculation circuit 602 and is configured to receive theplurality of normalized displacement values ξ_(k) from the displacementcalculation circuit 602, over a correlation output path 610. In someembodiments, the output generation circuit 604 is further configured toreceive the IQ distance d and the rotation angle ϕ₀ from thedisplacement calculation circuit 602. Upon receiving the plurality ofnormalized displacement values ξ_(k), the IQ distance d and the rotationangle ϕ₀, the output generation circuit 604 is further configured todetermine a plurality of output phase angles and a plurality of outputradius values, in order to generate a plurality of interpolated outputsamples (e.g., the interpolated output samples 218 b in FIG. 2) at thehigher sampling rate. In some embodiments, the output generation circuit604 is configured to generate both the plurality of output phase anglesand the plurality of output radius values, however, in otherembodiments, the output generation circuit 604 can be configured togenerate either the plurality of output phase angles or the plurality ofoutput radius values, associated with the plurality of interpolatedoutput samples. In some embodiments, the plurality of output phaseangles is determined based on equation (4) above and the plurality ofoutput radius values is determined based on equation (6) above byapplying the plurality of normalized displacement values ξ_(k). In oneexample embodiment, the arctan(ξ) function in equation (4) and the√{square root over (1+ξ²)} function in equation (6) above are realizedwithin the output generation circuit 604 using a lookup table (LUT), thedetails of which are given in FIG. 7 below. However, in otherembodiments, the arctan(ξ) function in equation (4) and the √{squareroot over (1+ξ²)} function in equation (6) above can be realizeddifferently, and the plurality of interpolated output samples can bedetermined using suitable approximation algorithms.

FIG. 7 depicts a block diagram of a lookup table (LUT) interpolationcircuit 700, according to one embodiment of the disclosure. In someembodiments, the LUT interpolation circuit 700 depicts a possible way ofimplementation of the mapped linear interpolation circuit 600 in FIG. 6.In this embodiment, the LUT interpolation circuit 700 is explained withrespect to the mapped linear interpolation circuit 600 in FIG. 6 and theprinciple of operation explained in FIG. 4a , FIG. 4b and FIG. 5. Themapped linear interpolation circuit 700 comprises an address generationcircuit 702 and an LUT circuit 704. In some embodiments, the addressgeneration circuit 702 is similar to the displacement calculationcircuit 602 in FIG. 6 and is configured to generate a plurality of LUTindex values ξ_(k). In some embodiments, the plurality of LUT indexvalues ξ_(k) correspond to the plurality of normalized displacementvalues ξ_(k) in FIG. 6 above. In some embodiments, the LUT circuit 704depicts on possible way of implementation of the output generationcircuit 604 in FIG. 6 and can replace the output generation circuit 604in some embodiments.

The LUT circuit 704 comprises a LUT 704 a comprising a plurality ofnormalized phase angles and a plurality of normalized radius values,wherein each of the normalized phase angle and normalized radius valuehas a respective LUT index value associated therewith. Alternately, inother embodiments, the LUT 704 a can comprise either the plurality ofnormalized phase angles or the plurality of normalized radius values,having the respective LUT index associated therewith. In someembodiments, the LUT index described herein can be mapped to thenormalized displacement ξ. In some embodiments, the plurality ofnormalized phase angles and the plurality of normalized radius values inthe LUT 704 a are determined based on applying a plurality ofpredetermined LUT index values ξ to the arctan(ξ) in equation (4) and√{square root over (1+ξ²)} in equation (6), respectively. In someembodiments, the LUT 704 a defines one possible way of implementation ofthe arctan(ξ) in equation (4) and √{square root over (1+ξ²)} in equation(6). In some embodiments, the plurality of predetermined LUT indexvalues ξ, for example, the number of LUT index values and their wordlength, to be utilized for populating the LUT 704 a is determined basedon the required resolution. In some embodiments, only positive values ofthe arctan(ξ) in equation (4) and √{square root over (1+ξ²)} in equation(6) are stored in the LUT 704 a, due to the symmetry of the arctan(ξ)and the hyperbola function √{square root over (1+ξ²)}. Also, in someembodiments, the values for arctan(ξ) and √{square root over (1+ξ²)},for large values of are not stored in the LUT 704 a, as for large ξ, thevalues for the normalized phase angles are nearly constant and the radiiare linear with respect to ξ. In some embodiments, the LUT 704 a ispopulated with the plurality of normalized phase angles and theplurality of normalized radius values prior to receiving the input IQsignal (for example, when the LUT interpolator circuit 700 isinitialized), and is only changed when the resolution requirementchanges or for some other system level changes.

The address generation circuit 702 comprises an arithmetic circuit 702 aconfigured to receive an input IQ signal 706 (e.g., the input IQ signal216 in FIG. 2). In some embodiments, the input IQ signal 706 comprises aplurality of input IQ samples having a first sampling rate (e.g., abaseband rate or a lower sampling rate) associated therewith. In someembodiments, the arithmetic circuit 702 a is further configured toreceive a current interpolation ratio 708. Upon receiving the input IQsignal 706 and the current interpolation ratio 708, in some embodiments,the arithmetic circuit 702 a is configured to normalize the input IQsignal based on rotating the normal vectors of IQ trajectoriesassociated with the input IQ signal 706 on to an l-axis of a respectiveIQ plane, as shown in FIG. 4b above or to a Q-axis of the respective IQplane. For each IQ trajectory associated with the input IQ signal 706,the arithmetic circuit 702 a is further configured to determine IQtrajectory parameters comprising an IQ distance d, IQ trajectory lengthl, an IQ offset a and a rotation angle ϕ₀, as explained above withrespect to FIG. 4a above. In some embodiments, the IQ trajectoryparameters can be determined at the arithmetic circuit 702 a by using acoordinate rotation digital computer (CORDIC). Upon determining the IQtrajectory parameters, the arithmetic circuit 702 a is configured todetermine an initial LUT index value ξ₀ and a LUT difference indexcomprising a difference in LUT index value between successive LUT indexvalues, for each IQ trajectory associated with the input IQ signal. Insome embodiments, the initial LUT index value ξ₀ and the LUT differenceindex ξ_(Δ) for each IQ trajectory is determined at the arithmeticcircuit 702 a based on equations (7)-(12) above. In some embodiments,the initial LUT index value ξ₀ and the LUT difference index ξ_(Δ)correspond to the initial normalized displacement value ξ₀ and thedifference in normalized displacement ξ_(Δ) given in equations (11) and(12), respectively.

The address generation circuit 702 further comprises an integratorcircuit 702 b configured to receive the initial LUT index value ξ₀ andthe LUT difference index ξ_(Δ) from the arithmetic circuit 702 a anddetermine a set of LUT index values ξ_(k) based on equation (13) above.In some embodiments, the LUT index values ξ_(k) are generated at theintegrator circuit 702 b at a higher rate (e.g., the RF clock rate). Insome embodiments, the integrator circuit 702 b is further configured toprovide the set of LUT index values ξ_(k) to the LUT circuit 704, inorder to access a set of normalized phase angles or a set of normalizedradius values or both corresponding to the set of LUT index values ξ_(k)from the LUT 704 a. The LUT circuit 704 further comprises a computationcircuit 704 b configured to receive the set of normalized phase anglesor the set of normalized radius values or both corresponding to the setof LUT index values ξ_(k) from the LUT 704 a and generate interpolatedpolar samples (e.g., the interpolated polar samples 218 b in FIG. 2),based on implementing equations (4) and (6) above. In such embodiments,the values for arctan(ξ) and √{square root over (1+ξ²)} corresponding tothe set of LUT index values ξ_(k) are directly accessed from the LUT 704a for implementing the equations (4) and (6) above. In some embodiments,the computation circuit 704 b is further configured to receive rotationangle ϕ₀ and the IQ distance d from the arithmetic circuit 702 a, inorder to implement the equations (4) and (6) above.

FIG. 8 depicts an example implementation of a lookup table (LUT)interpolation circuit 800, according to one embodiment of thedisclosure. In some embodiments, the LUT interpolation circuit 800depicts one possible way of implementation of the LUT interpolationcircuit 700 in FIG. 7. However, other possible ways of implementation ofthe LUT interpolation circuit 700 is also contemplated to be within thescope of this disclosure. FIG. 8 is explained herein with reference tothe LUT interpolation circuit 700 in FIG. 7 and the principle ofoperation explained in FIG. 4a , FIG. 4b and FIG. 5. The LUTinterpolation circuit 800 comprises an arithmetic circuit 802, anintegrator circuit 804 and a LUT circuit 806. The arithmetic circuit 802depicts one possible way of implementation of the arithmetic circuit 702a in FIG. 7 and can be included within the arithmetic circuit 702 a inFIG. 7, in some embodiments.

The arithmetic circuit 802 comprises a coordinate rotation digitalcomputer CORDIC-0 802 a and a CORDIC-1 802 b configured to receiveinformation associated with an input IQ signal (e.g., the input IQsignal 706 in FIG. 7). In some embodiments, the CORDIC-0 is configuredto rotate a vector v (i.e. a normal vector to a current IQ trajectory)associated with the input IQ signal on to an l-axis and determine thevalues for a rotation angle ϕ₀ and an IQ trajectory length l, asexplained above in FIG. 4b . In some embodiments, the CORDIC-1 reusesthe rotation information of CORDIC-1 and rotate Pm (i.e., an IQ datapoint associated with the current IQ trajectory) associated with theinput IQ signal and determine an IQ offset a and an IQ distance d asexplained above in FIG. 4b . The arithmetic circuit 802 furthercomprises a numerically controlled oscillator (NCO) 802 c configured toreceive information on a current interpolation ratio (e.g., n⁻¹), wheren is the current interpolation ratio and generate a time offset t₀ for afirst RF sample for the current IQ trajectory and a total number of RFsamples (i.e., K at the output of the NCO 802 c in FIG. 8) on thecurrent IQ trajectory based on implementing equations (7) and (9),respectively.

The arithmetic circuit 802 further comprises an arithmetic core-1circuit 802 e configured to receive the IQ offset a, the IQ distance d,the time offset to and the IQ trajectory length l, and generate aninitial LUT index value ξ₀ based on implementing equation (11) above. Inaddition, the arithmetic circuit 802 comprises an arithmetic core-0circuit 802 d configured to receive the inverse interpolation ratio n⁻¹,the IQ distance d and the IQ trajectory length l, and generate an LUTdifference index ξ_(Δ), based on implementing equation (12) above.

The integrator circuit 804 is coupled to the arithmetic circuit 802 andis configured to receive initial LUT index value ξ0, the LUT differenceindex ξΔ and the total number of samples to be generated K from thearithmetic circuit 802. In some embodiments, the integrator circuit 804is further configured to generate a set of LUT index values ξk based onimplementing equation (13) above. In some embodiments, the integratorcircuit 804 operates at a higher rate (e.g., the RF rate) and generatethe set of LUT index values ξk at the RF rate. The LUT circuit 806 iscoupled to the integrator circuit 804 and is configured to receive theset of LUT index values ξk from the integrator circuit 804. The LUTcircuit 806 comprises a LUT 807 configured to store a plurality ofnormalized phase angles and a plurality of normalized radius values,each of the plurality of normalized phase angles and the plurality ofnormalized radius values having a respective LUT index value associatedtherewith. In some embodiments, the LUT index described herein can bemapped to the normalized displacement ξ. In some embodiments, theplurality of normalized phase angles and the plurality of normalizedradius values in the LUT 807 are determined based on applying aplurality of predetermined LUT index values ξ to the arctan(ξ) inequation (4) and √{square root over (1+ξ²)} in equation (6),respectively. In some embodiments, the LUT 807 comprises a first LUT 807a configured to store the plurality of normalized phase angles and asecond LUT 807 b configured to store the plurality of normalized radiusvalues.

In some embodiments, the LUT circuit 806 is further configured to accessa set of normalized phase angles and a set of normalized radius valuescorresponding to the set of LUT index values ξk from the first LUT 807 aand the second LUT 807 b, respectively. The LUT circuit 806 furthercomprises a computation circuit 808 configured to receive the set ofnormalized phase angles and the set of normalized radius valuescorresponding to the set of LUT index values ξ_(k) from the LUT 807 andgenerate interpolated polar samples (e.g., the interpolated polarsamples 218 b in FIG. 2), based on implementing equations (4) and (6)above. In some embodiments, the computation circuit 808 is furtherconfigured to receive rotation angle ϕ₀ and the IQ distance d from thearithmetic circuit 802, in order to implement the equations (4) and (6)above. In some embodiments, the estimation circuit 808 further comprisesa first estimation circuit 808 a configured to implement the equation(4) and a second estimation circuit 808 b configured to implement theequation (6), in order to generate a set of output phase angles and aset of output radius values, respectively associated with theinterpolated polar samples.

FIG. 9 illustrates a method 900 of interpolation of polar signals inradio frequency (RF) transmitters, according to one embodiment of thedisclosure. The method 900 is explained herein with reference to thepolar transmitter 100 in FIG. 1 and the polar transmitter 200 in FIG. 2.However, in other embodiments, the method 900 is applicable to any RFtransmitters. At 902, an input in-phase (I) quadrature (Q) signal (e.g.,the input IQ signal 110 in FIG. 1) comprising a plurality of input IQsamples having a first sampling rate associated therewith is received atan estimation circuit (e.g., the estimation circuit 102 in FIG. 1). At904, a selection metric value associated with a predetermined selectionmetric of an IQ trajectory associated with one or more input IQ samplesof the input IQ signal is calculated at the estimation circuit. In someembodiments, the selection metric value is indicative of a position ofthe IQ trajectory associated with one or more input IQ samples withrespect to the origin of an IQ plane associated therewith. At 906, theinput IQ signal and the selection metric value from the estimationcircuit is received at a selection circuit (e.g., the selection circuit104 in FIG. 1). At 908, the input IQ signal is adaptively provided bythe selection circuit to a first interpolation circuit (e.g., the firstinterpolation circuit 106) that implements a first interpolation methodor to a second interpolation circuit (e.g., the second interpolationcircuit 108) that implements a second, different interpolation method,for generating interpolated polar samples (e.g., the interpolated polarsamples 118 a or 118 b) at a second, different sampling rate, from theinput IQ signal, based on the selection metric value.

In some embodiments, the first interpolation circuit comprises a polarinterpolation circuit (e.g., the polar interpolation circuit 206 in FIG.2) and the second interpolation circuit comprises a mapped linearinterpolation circuit (e.g., the mapped linear interpolation circuit 208in FIG. 2). However, in other embodiments, the first interpolationcircuit can comprise a mapped linear interpolation circuit and thesecond interpolation circuit can comprise a polar interpolation circuit.In some embodiments, the selection circuit is configured to provide theinput IQ signal to the first interpolation circuit (i.e., the polarinterpolation circuit 206), when the selection metric value (e.g., an IQradius estimate) indicates that the IQ trajectory is farther away fromthe origin. Further, the selection circuit is configured to provide theinput IQ signal to the second interpolation circuit (i.e., the mappedlinear interpolation circuit 208), when the selection metric value(e.g., the IQ radius estimate) indicates that the IQ trajectory iscloser to the origin. However, in other embodiments, the selectioncircuit is configured to provide the input IQ signal to the firstinterpolation circuit or to the second interpolation circuit, based onpredetermined selection metric ranges, for example, a firstpredetermined metric range and a second, different predetermined metricrange.

FIG. 10 illustrates a method 1000 for a linear interpolator circuit,according to one embodiment of the disclosure. The method 1000 isexplained herein with reference to the linear interpolator circuit 600in FIG. 6. However, in other embodiments, the method 1000 can be appliedto any mapped linear interpolation circuit associated with polartransmitters. At 1002, an input IQ signal (e.g., the input IQ signal 606in FIG. 6) comprising a plurality of input IQ samples at a firstsampling rate (e.g., baseband rate) is received at a displacementcalculation circuit (e.g., the displacement calculation circuit 602 inFIG. 6). At 1004, a set of normalized displacement values ξ_(k)comprising a set of values associated with a normalized displacement ξ,is determined at the displacement calculation circuit, based on thereceived input IQ signal and an information of a required interpolationratio (e.g., the interpolation ratio 608 in FIG. 6). In someembodiments, the set of normalized displacement values is determinedbased on implementing the equations (7)-(13) above. At 1006, a set ofinterpolated polar samples at a higher sampling rate (e.g., RF rate) isgenerated at an output generation circuit (e.g., the output generationcircuit 604 in FIG. 6), based on a mapping between the set of thenormalized displacement values determined at the displacementcalculation circuit and predefined functions of the normalizeddisplacement indicative of phase angle values or radius values or bothof the interpolated polar samples (e.g., the interpolated polar samples612 in FIG. 6) associated with the input IQ signal. In some embodiments,the predefined functions of the normalized displacement comprise thearctan(ξ) in equation (4) and √{square root over (1+ξ²)} in equation (6)above. In some embodiments, mapping the set of the normalizeddisplacement values ξ_(k) determined at the displacement calculationcircuit to the predefined functions of the normalized displacement ξ isimplemented at the output generation circuit, based on equations (4) and(6) above.

FIG. 11 illustrates a method 1100 for a lookup table (LUT) interpolationcircuit, according to one embodiment of the disclosure. The method 1100is explained herein with reference to the LUT interpolator circuit 700in FIG. 7. However, in other embodiments, the method 1100 can be appliedto any mapped linear interpolation circuit associated with polartransmitters. At 1102, a plurality of normalized phase angles or aplurality of normalized radius values or both, each having a respectiveLUT index value associated therewith, is stored in a LUT (e.g., the LUT704 a in FIG. 7) associated with an LUT circuit (e.g., the LUT circuit704 in FIG. 7). In some embodiments, the plurality of normalized phaseangles and the plurality of normalized radius values in the LUT aredetermined based on applying a plurality of predetermined LUT indexvalues ξ to the arctan(ξ) in equation (4) and √{square root over (1+ξ²)}in equation (6), respectively. At 1104, an input IQ signal (e.g., theinput IQ signal 706 in FIG. 7) comprising a plurality of input IQsamples at a first sampling rate is received at an address generatingcircuit (e.g., the address generating circuit 702 in FIG. 7).

At 1106, a set of LUT index values that facilitates to access a set ofnormalized phase angles and a set of normalized radius valuescorresponding to the set of LUT index values from the LUT, is generatedat the address generation circuit (in particular, within the arithmeticcircuit 702 a and the integrator circuit 702 b). In some embodiments,the set of LUT index values is generated at the address generationcircuit based on the received input IQ signal and an information of arequired interpolation ratio, by utilizing equations (7)-(13) above. Insome embodiments, the set of normalized phase angles or the set ofnormalized radius values or both are accessed from the LUT based on amapping between the set of LUT index values generated at the addressgenerating circuit and the LUT index values associated with thenormalized phase angles and the normalized radius values stored in theLUT. At 1108, the set of normalized phase angles or the set ofnormalized radius values or both corresponding to the set of LUT indexvalues from the LUT is received at a computation circuit (e.g., thecomputation circuit 704 b in FIG. 7) associated with the LUT circuit anda set interpolated polar output samples at a second, different samplingrate is generated based on the received set of normalized phase anglesor the set of normalized radius values or both. In some embodiments, theset of interpolated polar output samples at a second, different samplingrate is generated at the computation circuit based on implementingequations (4) and (6) above. For example, a set of interpolated phaseangles are generated based on adding (or subtracting) a rotation angleϕ₀ to each normalized phase angle of the received set of normalizedphase angles, as shown in equation (4). Further, a set of output radiusvalues are generated based on multiplying each normalized radius valueof the received set of normalized radius values by an IQ distance d, asshown in equation (6). In such embodiments, the computation circuit isfurther configured to receive rotation angle ϕ₀ and the IQ distance dfrom the address generation circuit, in order to implement the equations(4) and (6) above.

While the methods are illustrated, and described above as a series ofacts or events, it will be appreciated that the illustrated ordering ofsuch acts or events are not to be interpreted in a limiting sense. Forexample, some acts may occur in different orders and/or concurrentlywith other acts or events apart from those illustrated and/or describedherein. In addition, not all illustrated acts may be required toimplement one or more aspects or embodiments of the disclosure herein.Also, one or more of the acts depicted herein may be carried out in oneor more separate acts and/or phases.

While the apparatus has been illustrated and described with respect toone or more implementations, alterations and/or modifications may bemade to the illustrated examples without departing from the spirit andscope of the appended claims. In particular regard to the variousfunctions performed by the above described components or structures(assemblies, devices, circuits, systems, etc.), the terms (including areference to a “means”) used to describe such components are intended tocorrespond, unless otherwise indicated, to any component or structurewhich performs the specified function of the described component (e.g.,that is functionally equivalent), even though not structurallyequivalent to the disclosed structure which performs the function in theherein illustrated exemplary implementations of the invention.

In particular regard to the various functions performed by the abovedescribed components (assemblies, devices, circuits, systems, etc.), theterms (including a reference to a “means”) used to describe suchcomponents are intended to correspond, unless otherwise indicated, toany component or structure which performs the specified function of thedescribed component (e.g., that is functionally equivalent), even thoughnot structurally equivalent to the disclosed structure which performsthe function in the herein illustrated exemplary implementations of thedisclosure. In addition, while a particular feature may have beendisclosed with respect to only one of several implementations, suchfeature may be combined with one or more other features of the otherimplementations as may be desired and advantageous for any given orparticular application.

Examples can include subject matter such as a method, means forperforming acts or blocks of the method, at least one machine-readablemedium including instructions that, when performed by a machine causethe machine to perform acts of the method or of an apparatus or systemfor concurrent communication using multiple communication technologiesaccording to embodiments and examples described herein.

Example 1 is an apparatus for interpolation of polar signals in RFtransmitters, comprising an estimation circuit configured to receive aninput in-phase (I) quadrature (Q) signal comprising a plurality of inputIQ samples having a first sampling rate associated therewith; anddetermine a selection metric value associated with a predeterminedselection metric, based on the input IQ signal, wherein the selectionmetric value is indicative of a position of an IQ trajectory associatedwith one or more input IQ samples of the input IQ signal with respect tothe origin of an IQ plane; and a selection circuit coupled to theestimation circuit, and configured to receive the input IQ signal andthe selection metric value; and adaptively provide the input IQ signalto a first interpolation circuit that implements a first interpolationmethod or to a second interpolation circuit that implements a second,different interpolation method for generating interpolated polar samplesat a second, different sampling rate, from the input IQ signal, based onthe selection metric value.

Example 2 is an apparatus including the subject matter of claim 1,wherein the first interpolation circuit comprises a mapped linearinterpolation circuit configured to implement a mapped linearinterpolation method comprising generating the interpolated polarsamples at the second sampling rate comprising a higher sampling ratefrom the input IQ signal at the first sampling rate comprising a lowersampling rate, based on a mapping from IQ samples associated with IQtrajectories of the input IQ signal to polar samples at the highersampling rate based on one or more predefined functions indicative ofpolar representation of the IQ samples.

Example 3 is an apparatus including the subject matter of claims 1-2,including or omitting elements, wherein the selection circuit isconfigured to provide the input IQ signal to the mapped linearinterpolation circuit, when the selection metric value is within a firstpredetermined range.

Example 4 is an apparatus including the subject matter of claims 1-3,including or omitting elements, wherein the second interpolation circuitcomprises a polar interpolation circuit configured to implement a polarinterpolation method comprising converting the input IQ signal at thelower sampling rate into polar samples at the lower sampling rate,thereby forming low rate polar samples and interpolating the low ratepolar samples to generate the interpolated polar samples at the highersampling rate.

Example 5 is an apparatus including the subject matter of claims 1-4,including or omitting elements, wherein the selection circuit isconfigured to provide the input IQ signal to the polar interpolationcircuit, when the selection metric value is within a second, differentpredetermined range.

Example 6 is an apparatus including the subject matter of claims 1-5,including or omitting elements, wherein the selection metric valuecomprises an IQ radius estimate comprising a distance of the IQtrajectory from the origin of the IQ plane.

Example 7 is an apparatus including the subject matter of claims 1-6,including or omitting elements, wherein the first predetermined metricrange comprises IQ radius estimates between a predetermined metricthreshold and a predetermined value lower than the predetermined metricthreshold, and the second predetermined metric range comprises IQ radiusestimates between the predetermined metric threshold and a predeterminedvalue higher than the predetermined metric threshold.

Example 8 is an apparatus including the subject matter of claims 1-7,including or omitting elements, wherein the mapped linear interpolationcircuit comprises a displacement calculation circuit configured toreceive the input IQ signal; and determine a set of normalizeddisplacement values, based on the received input IQ signal and aninformation of a required interpolation ratio, wherein the set ofnormalized displacement values is associated with the higher samplingrate; and an output generation circuit configured to generate a set ofinterpolated polar samples at the higher sampling rate based on acorrelation between the set of the normalized displacement valuesdetermined at the displacement calculation circuit and the predefinedfunctions comprising predefined functions of the normalized displacementindicative of phase angle values of the interpolated polar samples orradius values of the interpolated polar samples or both, associated withthe input IQ signal.

Example 9 is an apparatus including the subject matter of claims 1-8,including or omitting elements, wherein the displacement calculationcircuit is further configured to normalize the input IQ signal based ona rotation of an IQ trajectory or a vector associated with the IQtrajectory, associated with the input IQ signal; and determine a numberof the interpolated polar samples to be generated for the IQ trajectory,an initial time offset of the interpolated polar samples and a timedifference between successive interpolated polar samples, based on theinterpolation ratio, in order to determine the set of the normalizeddisplacement values, wherein the number of the interpolated polarsamples to be generated for the IQ trajectory corresponds to a number ofnormalized displacement values in the set of normalized displacementvalues generated at the displacement calculation circuit.

Example 10 is an apparatus including the subject matter of claims 1-9,including or omitting elements, wherein the predefined functions of thenormalized displacement comprises a predefined phase angle function thatfacilitates to determine a phase angle associated with an interpolatedpolar sample, based on an information of a normalized displacementvalue.

Example 11 is an apparatus including the subject matter of claims 1-10,including or omitting elements, wherein the predefined functions of thenormalized displacement further comprises a predefined radius functionthat facilitates to determine a radius associated with the interpolatedpolar sample, based on an information of a normalized displacementvalue.

Example 12 is an apparatus including the subject matter of claims 1-11,including or omitting elements, wherein generating the set ofinterpolated polar samples comprises determining a phase angle or aradius value or both corresponding to each of the interpolated polarsamples of the set, based on the predefined phase angle function and thepredefined radius function.

Example 13 is an apparatus including the subject matter of claims 1-12,including or omitting elements, wherein the output generation circuitcomprises a lookup table (LUT) configured to store a plurality of phaseangles or a plurality of radius values or both associated with the IQtrajectory, wherein each of the plurality of the phase angles and theradius values are determined based on the predefined phase anglefunction and the predefined radius function, respectively, and whereineach of the phase angles and the radius values in the LUT is associatedwith a respective LUT index value that corresponds to a normalizeddisplacement value.

Example 14 is an apparatus including the subject matter of claims 1-13,including or omitting elements, wherein the set of interpolated polarsamples is generated at the output generation circuit based on accessinga set of phase angles or a set of radius values or both corresponding toa set of LUT index values from LUT, wherein the set of LUT index valuescorresponds to the set of normalized displacement values determined atthe displacement calculation circuit.

Example 15 is an apparatus including the subject matter of claims 1-14,including or omitting elements, wherein the output generation circuitfurther comprises a computation circuit configured to receive the set ofphase angles or the set of radius values or both corresponding to theset of LUT index values from LUT, and generate the set of interpolatedpolar samples by utilizing one or more parameters associated with arotation of an IQ trajectory associated with the input IQ signal.

Example 16 is a lookup table (LUT) based interpolator circuit,comprising a LUT circuit comprising an LUT configured to store aplurality of normalized phase angles or a plurality of normalized radiusvalues or both, wherein each of the normalized phase angle andnormalized radius value has a respective LUT index value associatedtherewith; and an address generating circuit configured to receive aninput IQ signal comprising a plurality of input IQ samples at a firstsampling rate; and generate a set of LUT index values at a second,different, sampling rate, in order to access a set of normalized phaseangles or a set of normalized radius values or both, corresponding tothe set of LUT index values from the LUT, wherein the set of LUT indexvalues is generated based on the received input IQ signal and aninformation of a required interpolation ratio.

Example 17 is a circuit including the subject matter of claim 16,wherein the address generating circuit further comprises an arithmeticcircuit configured to determine an initial LUT index value and a LUTdifference index comprising a difference in LUT index value betweensuccessive LUT index values, in order to generate the set of LUT indexvalues, based on a rotation of an IQ vector associated with twosuccessive IQ samples of the input IQ signal and the information of therequired interpolation ratio.

Example 18 is a circuit including the subject matter of claims 16-17,including or omitting elements, wherein the address generating circuitfurther comprises an integrator circuit coupled to the arithmeticcircuit and configured to generate the set of LUT index values based onthe initial LUT index value, the LUT difference index and a number ofinterpolated polar samples required for the current IQ vector, whereinthe number of interpolated polar samples is determined based on therequired interpolation ratio.

Example 19 is a circuit including the subject matter of claims 16-18,including or omitting elements, wherein the LUT circuit furthercomprises computation circuit configured to receive the set ofnormalized phase angles or the set of normalized radius values or bothcorresponding to the set of LUT index values from the LUT and generate aset interpolated polar output samples at the second, different samplingrate based thereon.

Example 20 is a circuit including the subject matter of claims 16-19,including or omitting elements, wherein generating the interpolatedpolar output samples at the computation circuit comprises generating aset of output phase angles associated with the interpolated polar outputsamples based on modifying each of the set of normalized phase angles bya rotation angle associated with the IQ vector; and generating a set ofoutput radius values associated with the interpolated polar outputsamples based on modifying each of the set of normalized radius valuesby an IQ distance comprising a value of a distance of the IQ vector fromthe origin of the IQ plane.

Example 21 is a circuit including the subject matter of claims 16-20,including or omitting elements, wherein the LUT further comprises afirst LUT configured to store the plurality of normalized phase anglesand a second, different LUT configured to store the plurality ofnormalized radius values.

Example 22 is a circuit including the subject matter of claims 16-21,including or omitting elements, wherein the plurality of normalizedphase angles and the plurality of normalized radius values in the LUTare generated by applying a plurality of predetermined LUT index valuesto a predefined phase angle function and a predefined radius function,respectively, wherein the predefined phase angle function and thepredefined radius function are defined as functions of LUT index.

Example 23 is an apparatus for mapped linear interpolation of polarsignals in RF transmitters, comprising a displacement calculationcircuit configured to receive an input IQ signal comprising a pluralityof input IQ samples at a first sampling rate; and determine a set ofnormalized displacement values comprising a set of values associatedwith a normalized displacement, based on the received input IQ signaland an information of a required interpolation ratio; and an outputgeneration circuit configured to generate a set of interpolated polarsamples at a second, different sampling rate based on a mapping betweenthe set of the normalized displacement values, and one or morepredefined functions of the normalized displacement indicative of phaseangle values of the interpolated polar samples or radius values ofinterpolated polar samples or both, associated with the input IQ signal.

Example 24 is an apparatus including the subject matter of claim 23,wherein the displacement calculation circuit is further configured tonormalize the input IQ signal based on a rotation of an IQ trajectoryassociated with the input IQ signal; determine a number of theinterpolated polar samples to be generated for the IQ trajectory anddetermine a time difference between successive interpolated polarsamples to be generated, based on the interpolation ratio, prior todetermining the plurality of the normalized displacement values, whereinthe number of the interpolated polar samples to be generated for the IQtrajectory corresponds to a number of normalized displacement values inthe set of normalized displacement values generated at the displacementcalculation circuit.

Example 25 is an apparatus including the subject matter of claims 23-24,including or omitting elements, wherein the predefined functions of thenormalized displacement comprise a predefined phase angle function thatfacilitates to determine a phase angle associated with an interpolatedpolar sample, based on an information of a normalized displacement value

Example 26 is an apparatus including the subject matter of claims 23-25,including or omitting elements, wherein the predefined functions of thenormalized displacement further comprise a predefined radius functionthat facilitates to determine a radius associated with the interpolatedpolar sample, based on an information of a normalized displacementvalue.

Example 27 is an apparatus including the subject matter of claims 23-26,including or omitting elements, wherein generating the set ofinterpolated polar samples at the output generation circuit comprisesdetermining a phase angle or a radius value or both corresponding toeach of the interpolated polar samples of the set, based on a mappingbetween the normalized displacement values, and the predefined phaseangle function and the predefined radius function.

Various illustrative logics, logical blocks, modules, and circuitsdescribed in connection with aspects disclosed herein can be implementedor performed with a general-purpose processor, a digital signalprocessor (DSP), an application specific integrated circuit (ASIC), afield programmable gate array (FPGA) or other programmable logic device,discrete gate or transistor logic, discrete hardware components, or anycombination thereof designed to perform functions described herein. Ageneral-purpose processor can be a microprocessor, but, in thealternative, processor can be any conventional processor, controller,microcontroller, or state machine.

The above description of illustrated embodiments of the subjectdisclosure, including what is described in the Abstract, is not intendedto be exhaustive or to limit the disclosed embodiments to the preciseforms disclosed. While specific embodiments and examples are describedherein for illustrative purposes, various modifications are possiblethat are considered within the scope of such embodiments and examples,as those skilled in the relevant art can recognize.

In this regard, while the disclosed subject matter has been described inconnection with various embodiments and corresponding Figures, whereapplicable, it is to be understood that other similar embodiments can beused or modifications and additions can be made to the describedembodiments for performing the same, similar, alternative, or substitutefunction of the disclosed subject matter without deviating therefrom.Therefore, the disclosed subject matter should not be limited to anysingle embodiment described herein, but rather should be construed inbreadth and scope in accordance with the appended claims below.

1-25. (canceled)
 26. An apparatus for interpolation of polar signals inRF transmitters, comprises: an estimation circuit configured to: receivean input in-phase (I) quadrature (Q) signal comprising a plurality ofinput IQ samples having a first sampling rate associated therewith; anddetermine a selection metric value associated with a predeterminedselection metric, based on the input IQ signal, wherein the selectionmetric value is indicative of a position of an IQ trajectory associatedwith one or more input IQ samples of the input IQ signal with respect tothe origin of an IQ plane; and a selection circuit coupled to theestimation circuit, and configured to: receive the input IQ signal andthe selection metric value; and adaptively provide the input IQ signalto a first interpolation circuit that implements a first interpolationmethod or to a second interpolation circuit that implements a second,different interpolation method for generating interpolated polar samplesat a second, different sampling rate, from the input IQ signal, based onthe selection metric value.
 27. The apparatus of claim 26, wherein thefirst interpolation circuit comprises a mapped linear interpolationcircuit configured to implement a mapped linear interpolation methodcomprising generating the interpolated polar samples at the secondsampling rate comprising a higher sampling rate from the input IQ signalat the first sampling rate comprising a lower sampling rate, based on amapping from IQ samples associated with IQ trajectories of the input IQsignal to polar samples at the higher sampling rate based on one or morepredefined functions indicative of polar representation of the IQsamples.
 28. The apparatus of claim 27, wherein the selection circuit isconfigured to provide the input IQ signal to the mapped linearinterpolation circuit, when the selection metric value is within a firstpredetermined range.
 29. The apparatus of claim 28, wherein the secondinterpolation circuit comprises a polar interpolation circuit configuredto implement a polar interpolation method comprising converting theinput IQ signal at the lower sampling rate into polar samples at thelower sampling rate, thereby forming low rate polar samples andinterpolating the low rate polar samples to generate the interpolatedpolar samples at the higher sampling rate.
 30. The apparatus of claim29, wherein the selection circuit is configured to provide the input IQsignal to the polar interpolation circuit, when the selection metricvalue is within a second, different predetermined range.
 31. Theapparatus of claim 27, wherein the mapped linear interpolation circuitcomprises: a displacement calculation circuit configured to: receive theinput IQ signal; and determine a set of normalized displacement values,based on the received input IQ signal and an information of a requiredinterpolation ratio, wherein the set of normalized displacement valuesis associated with the higher sampling rate; and an output generationcircuit configured to: generate a set of interpolated polar samples atthe higher sampling rate based on a correlation between the set of thenormalized displacement values determined at the displacementcalculation circuit and the predefined functions comprising predefinedfunctions of the normalized displacement indicative of phase anglevalues of the interpolated polar samples or radius values of theinterpolated polar samples or both, associated with the input IQ signal.32. The apparatus of claim 31, wherein the displacement calculationcircuit is further configured to: normalize the input IQ signal based ona rotation of an IQ trajectory or a vector associated with the IQtrajectory, associated with the input IQ signal; and determine a numberof the interpolated polar samples to be generated for the IQ trajectory,an initial time offset of the interpolated polar samples and a timedifference between successive interpolated polar samples, based on theinterpolation ratio, in order to determine the set of the normalizeddisplacement values, wherein the number of the interpolated polarsamples to be generated for the IQ trajectory corresponds to a number ofnormalized displacement values in the set of normalized displacementvalues generated at the displacement calculation circuit.
 33. Theapparatus of claim 31, wherein the predefined functions of thenormalized displacement comprises a predefined phase angle function thatfacilitates to determine a phase angle associated with an interpolatedpolar sample, based on an information of a normalized displacementvalue.
 34. The apparatus of claim 33, wherein the predefined functionsof the normalized displacement further comprises a predefined radiusfunction that facilitates to determine a radius associated with theinterpolated polar sample, based on an information of a normalizeddisplacement value.
 35. The apparatus of claim 34, wherein generatingthe set of interpolated polar samples comprises determining a phaseangle or a radius value or both corresponding to each of theinterpolated polar samples of the set, based on the predefined phaseangle function and the predefined radius function.
 36. The apparatus ofclaim 34, wherein the output generation circuit comprises a lookup table(LUT) configured to store a plurality of phase angles or a plurality ofradius values or both associated with the IQ trajectory, wherein each ofthe plurality of the phase angles and the radius values are determinedbased on the predefined phase angle function and the predefined radiusfunction, respectively, and wherein each of the phase angles and theradius values in the LUT is associated with a respective LUT index valuethat corresponds to a normalized displacement value.
 37. The apparatusof claim 36, wherein the set of interpolated polar samples is generatedat the output generation circuit based on accessing a set of phaseangles or a set of radius values or both corresponding to a set of LUTindex values from LUT, wherein the set of LUT index values correspondsto the set of normalized displacement values determined at thedisplacement calculation circuit.
 38. The apparatus of claim 37, whereinthe output generation circuit further comprises a computation circuitconfigured to receive the set of phase angles or the set of radiusvalues or both corresponding to the set of LUT index values from LUT,and generate the set of interpolated polar samples by utilizing one ormore parameters associated with a rotation of an IQ trajectoryassociated with the input IQ signal.
 39. A lookup table (LUT) basedinterpolator circuit, comprises: a LUT circuit comprising an LUTconfigured to store a plurality of normalized phase angles or aplurality of normalized radius values or both, wherein each of thenormalized phase angle and normalized radius value has a respective LUTindex value associated therewith; and an address generating circuitconfigured to: receive an input IQ signal comprising a plurality ofinput IQ samples at a first sampling rate; and generate a set of LUTindex values at a second, different, sampling rate, in order to access aset of normalized phase angles or a set of normalized radius values orboth, corresponding to the set of LUT index values from the LUT, whereinthe set of LUT index values is generated based on the received input IQsignal and an information of a required interpolation ratio.
 40. Thecircuit of claim 39, wherein the address generating circuit furthercomprises an arithmetic circuit configured to determine an initial LUTindex value and a LUT difference index comprising a difference in LUTindex value between successive LUT index values, in order to generatethe set of LUT index values, based on a rotation of an IQ vectorassociated with two successive IQ samples of the input IQ signal and theinformation of the required interpolation ratio.
 41. The circuit ofclaim 40, wherein the address generating circuit further comprises anintegrator circuit coupled to the arithmetic circuit and configured togenerate the set of LUT index values based on the initial LUT indexvalue, the LUT difference index and a number of interpolated polarsamples required for the current IQ vector, wherein the number ofinterpolated polar samples is determined based on the requiredinterpolation ratio.
 42. The circuit of claim 41, wherein the LUTcircuit further comprises computation circuit configured to receive theset of normalized phase angles or the set of normalized radius values orboth corresponding to the set of LUT index values from the LUT andgenerate a set interpolated polar output samples at the second,different sampling rate based thereon.
 43. The circuit of claim 42,wherein generating the interpolated polar output samples at thecomputation circuit comprises: generating a set of output phase anglesassociated with the interpolated polar output samples based on modifyingeach of the set of normalized phase angles by a rotation angleassociated with the IQ vector; and generating a set of output radiusvalues associated with the interpolated polar output samples based onmodifying each of the set of normalized radius values by an IQ distancecomprising a value of a distance of the IQ vector from the origin of theIQ plane.
 44. The circuit of claim 39, wherein the LUT further comprisesa first LUT configured to store the plurality of normalized phase anglesand a second, different LUT configured to store the plurality ofnormalized radius values.
 45. The circuit of claim 39, wherein theplurality of normalized phase angles and the plurality of normalizedradius values in the LUT are generated by applying a plurality ofpredetermined LUT index values to a predefined phase angle function anda predefined radius function, respectively, wherein the predefined phaseangle function and the predefined radius function are defined asfunctions of LUT index.
 46. An apparatus for mapped linear interpolationof polar signals in RF transmitters, comprises: a displacementcalculation circuit configured to: receive an input IQ signal comprisinga plurality of input IQ samples at a first sampling rate; and determinea set of normalized displacement values comprising a set of valuesassociated with a normalized displacement, based on the received inputIQ signal and an information of a required interpolation ratio; and anoutput generation circuit configured to: generate a set of interpolatedpolar samples at a second, different sampling rate based on a mappingbetween the set of the normalized displacement values, and one or morepredefined functions of the normalized displacement indicative of phaseangle values of the interpolated polar samples or radius values ofinterpolated polar samples or both, associated with the input IQ signal.47. The apparatus of claim 46, wherein the displacement calculationcircuit is further configured to: normalize the input IQ signal based ona rotation of an IQ trajectory associated with the input IQ signal;determine a number of the interpolated polar samples to be generated forthe IQ trajectory and determine a time difference between successiveinterpolated polar samples to be generated, based on the interpolationratio, prior to determining the plurality of the normalized displacementvalues, wherein the number of the interpolated polar samples to begenerated for the IQ trajectory corresponds to a number of normalizeddisplacement values in the set of normalized displacement valuesgenerated at the displacement calculation circuit.
 48. The apparatus ofclaim 46, wherein the predefined functions of the normalizeddisplacement comprise a predefined phase angle function that facilitatesto determine a phase angle associated with an interpolated polar sample,based on an information of a normalized displacement value.
 49. Theapparatus of claim 46, wherein the predefined functions of thenormalized displacement further comprise a predefined radius functionthat facilitates to determine a radius associated with the interpolatedpolar sample, based on an information of a normalized displacementvalue.
 50. The apparatus of claim 46, wherein generating the set ofinterpolated polar samples at the output generation circuit comprisesdetermining a phase angle or a radius value or both corresponding toeach of the interpolated polar samples of the set, based on a mappingbetween the normalized displacement values, and the predefined phaseangle function and the predefined radius function.